Martin O'Neill's men open their European Championship journey against Zlatan Ibrahimovic and company in Paris on June 13 and King believes that three points could be enough to send Ireland through to the knock-out stage, with games against Belgium and Italy to follow.
However, the former Finn Harps and Derry City manager remains wary of Erik Hamren's side, who booked their place in the tournament with a hard-fought play-off victory over Denmark.
"Sweden are no mugs, make no mistake about that," King told RTE Radio One.
"Our Under-18s just lost [4-1] to them [on Saturday], but that's the beauty of the international game. There are times we will perform and get the win.
"Four teams get out who finish in third place. If we get a win, that's gold dust. If we start with a win, then we're there."
The Ireland team will fly to France on Wednesday, June 8 and they will be based at the Trianon Palace in Versailles, with training taking place at Stade de Montbauron.
King believes that it will be difficult for the players being away from their families for the duration and says that O'Neill will need to have "good staff" to help manage such difficulty.
"Now they're in to the waiting game, which can be difficult. You have 23 different types of people. You can have tension, it can be jovial, and managing that can be difficult," King noted.
"[Giovanni] Trapattoni was very strict, very severe. The old Italian way. I'm not sure how Martin and Roy will behave. If they have a relaxed attitude and allow people to have a drink, that's one way of doing it.
"The difficulty for people is being away from their family. Being away is hard to get used to. It's six to eight weeks.
"People who are playing and know they're playing are confident. But people who aren't playing, it's a long two months. Then you have the different lads in the squad and the staff as well.
"If you want to deal with it as manager, make sure you have good staff to delegate."